Previous |  Up |  Next

Article

Full entry | Fulltext not available (moving wall 24 months)      Feedback
Keywords:
credit default swaps; fast mean-reverting volatility; perturbation method
Summary:
We consider the pricing of credit default swaps (CDSs) with the reference asset assumed to follow a geometric Brownian motion with a fast mean-reverting stochastic volatility, which is often observed in the financial market. To establish the pricing mechanics of the CDS, we set up a default model, under which the fair price of the CDS containing the unknown ``no default'' probability is derived first. It is shown that the ``no default'' probability is equivalent to the price of a down-and-out binary option written on the same reference asset. Based on the perturbation approach, we obtain an approximated but closed-form pricing formula for the spread of the CDS. It is also shown that the accuracy of our solution is in the order of $\mathscr O(\epsilon )$.
References:
[1] Beckers, S.: Variances of security price returns based on high, low, and closing prices. J. Business 56 (1983), 97-112. DOI 10.1086/296188 | MR 2695462
[2] Brigo, D., Chourdakis, K.: Counterparty risk for credit default swaps: impact of spread volatility and default correlation. Int. J. Theor. Appl. Finance 12 (2009), 1007-1026. DOI 10.1142/S0219024909005567 | MR 2574492 | Zbl 1187.91206
[3] Cariboni, J., Schoutens, W.: Pricing credit default swaps under Lévy models. J. Comput. Finance 10 (2007), 71-91. DOI 10.21314/jcf.2007.172
[4] Malherbe, E. De: A simple probabilistic approach to the pricing of credit default swap covenants. J. Risk 8 (2006), 85-113. DOI 10.21314/jor.2006.130
[5] Duffie, D., Singleton, K. J.: An econometric model of the term structure of interest-rate swap yields. J. Finance 52 (1997), 1287-1321. DOI 10.1111/j.1540-6261.1997.tb01111.x
[6] Fouque, J.-P., Papanicolaou, G., Sircar, K. R.: Derivatives in Financial Markets with Stochastic Volatility, Cambridge University Press, Cambridge. (2000). MR 1768877 | Zbl 0954.91025
[7] Fouque, J.-P., Papanicolaou, G., Sircar, K. R.: Mean-reverting stochastic volatility. Int. J. Theor. Appl. Finance 3 (2000), 101-142. DOI 10.1142/S0219024900000061 | Zbl 1153.91497
[8] Fouque, J.-P., Papanicolaou, G., Sircar, K. R., Solna, K.: Singular perturbations in option pricing. SIAM J. Appl. Math. 63 (2003), 1648-1665. DOI 10.1137/S0036139902401550 | MR 2001213 | Zbl 1039.91024
[9] He, X., Chen, W.: The pricing of credit default swaps under a generalized mixed fractional Brownian motion. Physica A 404 (2014), 26-33. DOI /10.1016/j.physa.2014.02.046 | MR 3188756 | Zbl 1402.91847
[10] Jarrow, R. A., Turnbull, S. M.: Pricing derivatives on financial securities subject to credit risk. J. Finance 50 (1995), 53-86. DOI 10.1111/j.1540-6261.1995.tb05167.x
[11] Joy, R. C., Schlig, E. S.: Thermal properties of very fast transistors. IEEE Transactions on Electron Devices 17 (1970), 586-594. DOI 10.1109/t-ed.1970.17035
[12] Longstaff, F. A., Schwartz, E. S.: A simple approach to valuing risky fixed and floating rate debt. J. Finance 50 (1995), 789-819. DOI 10.1111/j.1540-6261.1995.tb04037.x
[13] Merton, R. C.: On the pricing of corporate debt: the risk structure of interest rates. J. Finance 29 (1974), 449-470. DOI 10.2307/2978814 | MR 3235242
[14] O'Kane, D., Turnbull, S.: Valuation of credit default swaps. QCR Quarterly 2003-Q1/Q2 (2003), 17 pages.
[15] Ramm, A. G.: A simple proof of the Fredholm alternative and a characterization of the Fredholm operators. Am. Math. Mon. 108 (2001), 855-860. DOI 10.2307/2695558 | MR 1864050 | Zbl 1036.47005
[16] Shreve, S. E.: Stochastic Calculus for Finance II. Continuous-Time Models. Springer Finance, Springer, New York (2004). MR 2057928 | Zbl 1068.91041
[17] Tavella, D., Randall, C.: Pricing Financial Instruments: The Tinite Difference Method. John Wiley & Sons, New York (2000).
[18] Zhou, C.: The term structure of credit spreads with jump risk. J. Banking & Finance 25 (2005), 2015-2040. DOI 10.1016/s0378-4266(00)00168-0
[19] Zhu, S.-P., Chen, W.-T.: Pricing perpetual American options under a stochastic-volatility model with fast mean reversion. Appl. Math. Lett. 24 (2011), 1663-1669. DOI 10.1016/j.aml.2011.04.011 | MR 2803003 | Zbl 1216.91035
Partner of
EuDML logo